Problem: Simplify the following expression: $\dfrac{66a^2}{30a^5}$ You can assume $a \neq 0$.
$ \dfrac{66a^2}{30a^5} = \dfrac{66}{30} \cdot \dfrac{a^2}{a^5} $ To simplify $\frac{66}{30}$ , find the greatest common factor (GCD) of $66$ and $30$ $66 = 2 \cdot 3 \cdot 11$ $30 = 2 \cdot 3 \cdot 5$ $ \mbox{GCD}(66, 30) = 2 \cdot 3 = 6 $ $ \dfrac{66}{30} \cdot \dfrac{a^2}{a^5} = \dfrac{6 \cdot 11}{6 \cdot 5} \cdot \dfrac{a^2}{a^5} $ $\phantom{ \dfrac{66}{30} \cdot \dfrac{2}{5}} = \dfrac{11}{5} \cdot \dfrac{a^2}{a^5} $ $ \dfrac{a^2}{a^5} = \dfrac{a \cdot a}{a \cdot a \cdot a \cdot a \cdot a} = \dfrac{1}{a^3} $ $ \dfrac{11}{5} \cdot \dfrac{1}{a^3} = \dfrac{11}{5a^3} $